On Mumford's construction of degenerating abelian varieties
alg-geom
2008-02-03 v2 Algebraic Geometry
Abstract
We prove that a 1-dimnl family of abelian varieties with an ample sheaf defining principal polarization can be canonically compactified (after a finite base change) to a projective family with an ample sheaf. We show that the central fiber (P,L), which we call an SQAV, has a canonical Cartier theta divisor. We give a combinatorial definition for SQAVs and describe their geometrical properties, in particular compute cohomologies of L^n, n\ge0.
Cite
@article{arxiv.alg-geom/9608014,
title = {On Mumford's construction of degenerating abelian varieties},
author = {Valery Alexeev and Iku Nakamura},
journal= {arXiv preprint arXiv:alg-geom/9608014},
year = {2008}
}
Comments
Final version, to appear in Tohoku Math. J